How to get the density matrix from a stabilizer table in qiskit

Question

I am new to qiskit and quantum computing in general, so bear with me please. For my bachelor's thesis, I am programming qiskit to first generate a random Clifford circuit (qc) and to then measure the output state once.

For that I am using

$\texttt{measurement = StabilizerState(qc).measure()}$

which returns a tuple, containing the measurement outcome and its stabilizer table, For example

$\texttt{(011, StabilizerTable: ['ZII', '-IZI', '-IIZ']).}$

Now I would like to apply the inverse Clifford circuit to the outcome state (thereby transforming the stabilizer table to [U†$\cdot$ZII$\cdot$U, -U†$\cdot$IZI$\cdot$U, -U†$\cdot$IIZ$\cdot$U], where U† is the global unitary representing the inverse Clifford circuit.) For that I am using

$\texttt{measurement[1].evolve(StabilizerState(qc.inverse())}$

which returns a new stabilizer table describing the transformed stabilizer state. I would now like to know some sort of representation of the new state, like its density matrix.

My question is: is there some way to get the underlying state vector or density matrix from a stabilizer table? My first idea, reading through the documentation was

$\texttt{StabilizerState(input).to_operator}$

which did not work since it only returns the input in form of an operator (for example qc).

I guess I could always just convert the first measurement result (011) into an array and calculate U† |011> <011| U the old fashioned way, which doesn't seem very efficient to me though.

Answer 1

EDIT: you can build the desired DensityMatrix starting from an empty $n$-qubits circuit (in the state $| \psi \rangle = | 0 \rangle^{\otimes n}$) and then use the DensityMatrix.evolve method passing your StabilizerState object:

from qiskit import QuantumCircuit
from qiskit.quantum_info import DensityMatrix, StabilizerState
from qiskit.visualization import array_to_latex

qc = QuantumCircuit(2)
rho = DensityMatrix(qc)
qc.h(0)
qc.x(1)
stabstate = StabilizerState(qc)
rho = rho.evolve(stabstate)

array_to_latex(rho)

$$ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & \tfrac{1}{2} & \tfrac{1}{2} \\ 0 & 0 & \tfrac{1}{2} & \tfrac{1}{2} \\ \end{bmatrix} $$

Answer 2

If your input state is $|000\rangle$, then you can easily get the output as a Statevector as follows:

sv = Statevector.from_label('000').evolve(stab)
sv.draw('latex')

Similarly, you can get the output as a DensityMatrix:

dm = DensityMatrix.from_label('000').evolve(stab)
dm.draw('latex')